THE PHENOMENA OF RUPTURE AND FLOW IN SOLIDS. 
177 
5. Deductions from the Foregoing Results. 
The estimate of maximum stress obtained above appears to lead to a peremptory 
disproof of the hypothesis that the maximum tension in this glass, at rupture, is always 
equal to the breaking stress in ordinary tensile tests. If Hooke’s law was obeyed to 
rupture, and the squares of the strains were negligible, the maximum tension in the 
above cracked tube could not have been less than 344,000 lbs. per sq. inch ; but, in 
the tensile tests, Hooke’s law was obeyed up to the breaking stress, the squares of 
the strains were negligible, and the maximum stress was only 24,900 lbs. per sq. inch. 
Hence the stresses could not have been the same in the two cases. Moreover, 
the order of the results obtained suggests (though this is not rigorously proved, 
as the assumptions have not been checked at stresses above 24,900 lbs. per sq. 
inch) that the actual strength may be more than ten times that given by the 
hypothesis. 
Similar conclusions may be drawn regarding the “ maximum extension,” “ maximum 
stress-difference ” and “ maximum shear strain ” hypotheses which have been proposed 
from time to time for estimating the strength of brittle solids. 
These conclusions suggest inquiries of the greatest interest. If the strength of this 
glass, as ordinarily interpreted, is not constant, on what does it depend ? What is 
the greatest possible strength, and can this strength be made available for technical 
purposes by appropriate treatment of the material ? Further, is the strength of other 
materials governed by similar considerations ? 
Some indication of the probable maximum strength of this glass may be obtained 
from the bursting tests already described. There is no reason for supposing that, in those 
tests, the radii of curvature at the corners of the cracks were as great as 2X10 -6 inch. 
It is much more likely that they were of the same order as the molecular dimensions. 
Considering, as before, the last bulb in Table II., and putting p = 2xl0~ 8 inch 
in formula (21), it is found that the maximum stress, F, is about 3X10 6 lbs. per 
sq. inch. Elastic theory cannot, of course, be expected to apply with much accuracy 
to cases where the dimensions are molecular, on account of the replacement of 
summation by integration, and the probable diminution of modulus at very high 
stresses must involve a further error. Taking these circumstances into consideration, 
however, it may still be said that the probable maximum strength of the glass used 
in the foregoing experiments is of the order 10 6 lbs. per sq. inch. 
It is of interest to enquire at this stage whether there is any reason for ascribing 
similar maximum strengths to other materials. On the molecular theory of matter 
the tensile strength of an isotropic solid or liquid is of the same order as, though less 
than, its “ intrinsic pressure,” and may therefore be estimated either from a knowledge 
of the total heat required to vaporise the substance or by means of Van der Waal’s 
equation.* It may be noted that these methods of estimating the stress indicate that 
* Poynting and Thomson, ‘ Properties of Matter,’ ch. xv. 
